Umm, yes, it does have an email log page, in the dashboard, under the tab marked “E-Mail” -> “Manage E-Mail”.
As for who hosts it, I do. I’m the SysAdmin trying to figure out why this thing doesn’t send emails. WordPress was set up by one of my developers (unfortunately).
Nothing appears in the server’s logs, which is part of the problem. I’ve tried using the underlying server’s Sendmail to send emails out. I’ve tried relaying it through one of my other servers, using SMTP. No luck there.
So, I’ve come here looking for help.